MinT - Best Known (116, 116+109, s)-Nets in Base 4

Best Known (116, 116+109, s)-Nets in Base 4

(116, 116+109, 130)-Net over F₄ — Constructive and digital

Digital (116, 225, 130)-net over F₄, using

t-expansion [i] based on digital (105, 225, 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]

(116, 116+109, 176)-Net over F₄ — Digital

Digital (116, 225, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+109, 2152)-Net in Base 4 — Upper bound on s

There is no (116, 225, 2153)-net in base 4, because

1 times m-reduction [i] would yield (116, 224, 2153)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 727 360770 780596 077653 016211 386336 133240 737704 430009 393141 787231 030271 703476 743945 116576 897731 326835 972385 286763 128413 003002 976294 128400 > 4²²⁴ [i]