MinT - Best Known (78, 231, s)-Nets in Base 4

Best Known (78, 231, s)-Nets in Base 4

(78, 231, 104)-Net over F₄ — Constructive and digital

Digital (78, 231, 104)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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, 231, 112)-Net over F₄ — Digital

Digital (78, 231, 112)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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, 231, 583)-Net in Base 4 — Upper bound on s

There is no (78, 231, 584)-net in base 4, because

1 times m-reduction [i] would yield (78, 230, 584)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 107050 873179 930897 348282 951046 345045 386947 656273 767184 571779 496758 948610 287659 909277 230475 914533 603848 457874 081870 374801 700887 389070 904256 > 4²³⁰ [i]