MinT - Best Known (76, 76+105, s)-Nets in Base 4

Best Known (76, 76+105, s)-Nets in Base 4

(76, 76+105, 104)-Net over F₄ — Constructive and digital

Digital (76, 181, 104)-net over F₄, using

t-expansion [i] based on digital (73, 181, 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+105, 112)-Net over F₄ — Digital

Digital (76, 181, 112)-net over F₄, using

t-expansion [i] based on digital (73, 181, 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+105, 776)-Net in Base 4 — Upper bound on s

There is no (76, 181, 777)-net in base 4, because

1 times m-reduction [i] would yield (76, 180, 777)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 479736 866167 447463 267988 727367 436870 340719 941391 055488 732445 176087 656173 081458 950663 393203 095871 442921 751200 > 4¹⁸⁰ [i]