MinT - Best Known (124−39, 124, s)-Nets in Base 4

Best Known (124−39, 124, s)-Nets in Base 4

(124−39, 124, 240)-Net over F₄ — Constructive and digital

Digital (85, 124, 240)-net over F₄, using

2 times m-reduction [i] based on digital (85, 126, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 42, 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]

(124−39, 124, 465)-Net over F₄ — Digital

Digital (85, 124, 465)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−39, 124, 20860)-Net in Base 4 — Upper bound on s

There is no (85, 124, 20861)-net in base 4, because

1 times m-reduction [i] would yield (85, 123, 20861)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 145614 716766 253439 172559 305349 995244 763088 266186 736624 632163 058572 792140 > 4¹²³ [i]