MinT - Best Known (252−123, 252, s)-Nets in Base 4

Best Known (252−123, 252, s)-Nets in Base 4

(252−123, 252, 130)-Net over F₄ — Constructive and digital

Digital (129, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(252−123, 252, 190)-Net over F₄ — Digital

Digital (129, 252, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−123, 252, 2307)-Net in Base 4 — Upper bound on s

There is no (129, 252, 2308)-net in base 4, because

1 times m-reduction [i] would yield (129, 251, 2308)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 281514 005575 031118 616680 915858 207021 755221 324442 327311 419915 802768 374614 014934 004827 193060 753598 298420 101666 904360 600106 233815 533220 198959 679520 180160 > 4²⁵¹ [i]