MinT - Best Known (86, 231, s)-Nets in Base 4

Best Known (86, 231, s)-Nets in Base 4

(86, 231, 104)-Net over F₄ — Constructive and digital

Digital (86, 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]

(86, 231, 129)-Net over F₄ — Digital

Digital (86, 231, 129)-net over F₄, using

t-expansion [i] based on digital (81, 231, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(86, 231, 714)-Net in Base 4 — Upper bound on s

There is no (86, 231, 715)-net in base 4, because

1 times m-reduction [i] would yield (86, 230, 715)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 216294 306772 708648 180306 837681 271889 692956 898314 977351 836220 262622 046320 225636 604640 719976 478446 072653 137634 292035 478089 320347 249891 648075 > 4²³⁰ [i]