MinT - Best Known (107−76, 107, s)-Nets in Base 27

Best Known (107−76, 107, s)-Nets in Base 27

(107−76, 107, 114)-Net over F₂₇ — Constructive and digital

Digital (31, 107, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 107, 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]

(107−76, 107, 150)-Net in Base 27 — Constructive

(31, 107, 150)-net in base 27, using

1 times m-reduction [i] based on (31, 108, 150)-net in base 27, using
- base change [i] based on digital (4, 81, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(107−76, 107, 208)-Net over F₂₇ — Digital

Digital (31, 107, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 107, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(107−76, 107, 6178)-Net in Base 27 — Upper bound on s

There is no (31, 107, 6179)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1440 617496 267133 700310 111290 430711 904090 954860 319909 188725 072222 773482 999387 988010 252715 585004 622968 604302 431859 211323 497712 136685 849459 654063 689767 122573 > 27¹⁰⁷ [i]