MinT - Best Known (78, 78+112, s)-Nets in Base 4

Best Known (78, 78+112, s)-Nets in Base 4

(78, 78+112, 104)-Net over F₄ — Constructive and digital

Digital (78, 190, 104)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(78, 78+112, 112)-Net over F₄ — Digital

Digital (78, 190, 112)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(78, 78+112, 753)-Net in Base 4 — Upper bound on s

There is no (78, 190, 754)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 599775 267516 363774 361829 124564 145851 822265 201198 941437 324120 164969 703019 154378 476785 572025 798187 169841 751107 722952 > 4¹⁹⁰ [i]