MinT - Best Known (76, 76+159, s)-Nets in Base 4

Best Known (76, 76+159, s)-Nets in Base 4

(76, 76+159, 104)-Net over F₄ — Constructive and digital

Digital (76, 235, 104)-net over F₄, using

t-expansion [i] based on digital (73, 235, 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]

(76, 76+159, 112)-Net over F₄ — Digital

Digital (76, 235, 112)-net over F₄, using

t-expansion [i] based on digital (73, 235, 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]

(76, 76+159, 548)-Net in Base 4 — Upper bound on s

There is no (76, 235, 549)-net in base 4, because

1 times m-reduction [i] would yield (76, 234, 549)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 765 199951 882157 844355 258540 641419 267858 421768 854017 348939 265171 984433 871352 674729 954584 646506 352458 034353 559588 700811 800567 183289 850832 572672 > 4²³⁴ [i]