MinT - Best Known (213−70, 213, s)-Nets in Base 4

Best Known (213−70, 213, s)-Nets in Base 4

(213−70, 213, 240)-Net over F₄ — Constructive and digital

Digital (143, 213, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 71, 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]

(213−70, 213, 612)-Net over F₄ — Digital

Digital (143, 213, 612)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−70, 213, 21356)-Net in Base 4 — Upper bound on s

There is no (143, 213, 21357)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 499631 055370 632013 881409 546656 899643 284987 851655 859687 286337 588794 820972 434498 445452 585366 416710 892029 698068 464273 204438 626340 > 4²¹³ [i]