MinT - Best Known (185−87, 185, s)-Nets in Base 4

Best Known (185−87, 185, s)-Nets in Base 4

(185−87, 185, 104)-Net over F₄ — Constructive and digital

Digital (98, 185, 104)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(185−87, 185, 163)-Net over F₄ — Digital

Digital (98, 185, 163)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−87, 185, 2086)-Net in Base 4 — Upper bound on s

There is no (98, 185, 2087)-net in base 4, because

1 times m-reduction [i] would yield (98, 184, 2087)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 611 063003 625136 019328 091712 840631 613664 158064 904494 804922 962569 066108 099441 814230 357584 126328 228299 484294 205440 > 4¹⁸⁴ [i]