MinT - Best Known (77, 77+126, s)-Nets in Base 4

Best Known (77, 77+126, s)-Nets in Base 4

(77, 77+126, 104)-Net over F₄ — Constructive and digital

Digital (77, 203, 104)-net over F₄, using

t-expansion [i] based on digital (73, 203, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(77, 77+126, 112)-Net over F₄ — Digital

Digital (77, 203, 112)-net over F₄, using

t-expansion [i] based on digital (73, 203, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(77, 77+126, 654)-Net in Base 4 — Upper bound on s

There is no (77, 203, 655)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 166 047253 037210 496698 711018 883232 622405 746792 787103 665934 979054 831644 607397 272320 095931 001283 728736 522294 466861 041662 043680 > 4²⁰³ [i]