MinT - Best Known (183−69, 183, s)-Nets in Base 4

Best Known (183−69, 183, s)-Nets in Base 4

(183−69, 183, 130)-Net over F₄ — Constructive and digital

Digital (114, 183, 130)-net over F₄, using

t-expansion [i] based on digital (105, 183, 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]

(183−69, 183, 331)-Net over F₄ — Digital

Digital (114, 183, 331)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(183−69, 183, 7508)-Net in Base 4 — Upper bound on s

There is no (114, 183, 7509)-net in base 4, because

1 times m-reduction [i] would yield (114, 182, 7509)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 696747 236408 414920 332153 402626 722863 966554 444068 508409 032100 222160 289083 983178 757320 884042 548532 660778 877772 > 4¹⁸² [i]