MinT - Best Known (151, 151+63, s)-Nets in Base 4

Best Known (151, 151+63, s)-Nets in Base 4

(151, 151+63, 531)-Net over F₄ — Constructive and digital

Digital (151, 214, 531)-net over F₄, using

2 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 72, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(151, 151+63, 950)-Net over F₄ — Digital

Digital (151, 214, 950)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+63, 56682)-Net in Base 4 — Upper bound on s

There is no (151, 214, 56683)-net in base 4, because

1 times m-reduction [i] would yield (151, 213, 56683)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 296377 033069 161797 616010 049270 613579 949785 230027 293949 924546 006132 613851 800417 230627 687346 154960 344640 951108 171714 057656 568000 > 4²¹³ [i]