MinT - Best Known (123, 248, s)-Nets in Base 4

Best Known (123, 248, s)-Nets in Base 4

(123, 248, 130)-Net over F₄ — Constructive and digital

Digital (123, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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]

(123, 248, 170)-Net over F₄ — Digital

Digital (123, 248, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 248, 1946)-Net in Base 4 — Upper bound on s

There is no (123, 248, 1947)-net in base 4, because

1 times m-reduction [i] would yield (123, 247, 1947)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52015 106510 369675 200116 019647 580290 542225 640285 582362 869438 206016 133126 753835 319582 102280 981596 968318 366726 770551 029779 210753 328987 568913 896130 109280 > 4²⁴⁷ [i]