MinT - Best Known (34, 34+68, s)-Nets in Base 27

Best Known (34, 34+68, s)-Nets in Base 27

(34, 34+68, 114)-Net over F₂₇ — Constructive and digital

Digital (34, 102, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 102, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(34, 34+68, 172)-Net in Base 27 — Constructive

(34, 102, 172)-net in base 27, using

6 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(34, 34+68, 220)-Net over F₂₇ — Digital

Digital (34, 102, 220)-net over F₂₇, using

t-expansion [i] based on digital (33, 102, 220)-net over F₂₇, using
- net from sequence [i] based on digital (33, 219)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 33 and N(F) ≥ 220, using
    - Drinfeld modules of rank 1 [i]

(34, 34+68, 226)-Net in Base 27

(34, 102, 226)-net in base 27, using

2 times m-reduction [i] based on (34, 104, 226)-net in base 27, using
- base change [i] based on digital (8, 78, 226)-net over F₈₁, using
  - net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
      - a curve from the manYPoints database [i]

(34, 34+68, 10229)-Net in Base 27 — Upper bound on s

There is no (34, 102, 10230)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 100 085736 621340 779795 051758 316813 640842 970052 057741 066622 726702 005584 886538 709240 591492 562884 440867 956619 907951 479663 244322 209714 889995 166878 732557 > 27¹⁰² [i]