MinT - Best Known (122, 122+55, s)-Nets in Base 4

Best Known (122, 122+55, s)-Nets in Base 4

(122, 122+55, 312)-Net over F₄ — Constructive and digital

Digital (122, 177, 312)-net over F₄, using

t-expansion [i] based on digital (121, 177, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 59, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(122, 122+55, 649)-Net over F₄ — Digital

Digital (122, 177, 649)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+55, 30585)-Net in Base 4 — Upper bound on s

There is no (122, 177, 30586)-net in base 4, because

1 times m-reduction [i] would yield (122, 176, 30586)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9179 784321 171826 174236 030344 755627 171757 711439 985642 530013 435415 527498 483599 587428 417162 751507 332289 709088 > 4¹⁷⁶ [i]