MinT - Best Known (34, 110, s)-Nets in Base 27

Best Known (34, 110, s)-Nets in Base 27

(34, 110, 114)-Net over F₂₇ — Constructive and digital

Digital (34, 110, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 110, 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, 110, 160)-Net in Base 27 — Constructive

(34, 110, 160)-net in base 27, using

27² times duplication [i] based on (32, 108, 160)-net in base 27, using
- base change [i] based on digital (5, 81, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(34, 110, 220)-Net over F₂₇ — Digital

Digital (34, 110, 220)-net over F₂₇, using

t-expansion [i] based on digital (33, 110, 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, 110, 8019)-Net in Base 27 — Upper bound on s

There is no (34, 110, 8020)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 190004 841872 244363 166712 861233 801712 195093 499318 040748 986939 479948 200580 382788 180599 415847 689112 976472 059381 034052 084857 838996 390242 726270 196151 234025 201593 > 27¹¹⁰ [i]