MinT - Best Known (124, 124+123, s)-Nets in Base 4

Best Known (124, 124+123, s)-Nets in Base 4

(124, 124+123, 130)-Net over F₄ — Constructive and digital

Digital (124, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(124, 124+123, 176)-Net over F₄ — Digital

Digital (124, 247, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+123, 2054)-Net in Base 4 — Upper bound on s

There is no (124, 247, 2055)-net in base 4, because

1 times m-reduction [i] would yield (124, 246, 2055)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13054 170438 603287 714831 395376 117210 653692 166874 780838 346451 132709 293883 244808 892610 883113 610076 100390 272496 633546 958318 498906 720495 508748 840885 938688 > 4²⁴⁶ [i]