MinT - Best Known (124, 124+59, s)-Nets in Base 4

Best Known (124, 124+59, s)-Nets in Base 4

(124, 124+59, 240)-Net over F₄ — Constructive and digital

Digital (124, 183, 240)-net over F₄, using

t-expansion [i] based on digital (123, 183, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 61, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(124, 124+59, 577)-Net over F₄ — Digital

Digital (124, 183, 577)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+59, 23334)-Net in Base 4 — Upper bound on s

There is no (124, 183, 23335)-net in base 4, because

1 times m-reduction [i] would yield (124, 182, 23335)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 580800 278956 491029 853453 232815 862875 157096 703294 143235 242592 528312 367398 695556 029449 729488 353112 948433 575448 > 4¹⁸² [i]