MinT - Best Known (113, 113+73, s)-Nets in Base 4

Best Known (113, 113+73, s)-Nets in Base 4

(113, 113+73, 130)-Net over F₄ — Constructive and digital

Digital (113, 186, 130)-net over F₄, using

t-expansion [i] based on digital (105, 186, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(113, 113+73, 292)-Net over F₄ — Digital

Digital (113, 186, 292)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+73, 5879)-Net in Base 4 — Upper bound on s

There is no (113, 186, 5880)-net in base 4, because

1 times m-reduction [i] would yield (113, 185, 5880)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2407 173736 444100 864720 003710 228951 745246 073593 519441 219197 099903 274369 847546 251545 966779 918725 100586 207239 489499 > 4¹⁸⁵ [i]