MinT - Best Known (85, 85+37, s)-Nets in Base 4

Best Known (85, 85+37, s)-Nets in Base 4

(85, 85+37, 312)-Net over F₄ — Constructive and digital

Digital (85, 122, 312)-net over F₄, using

1 times m-reduction [i] based on digital (85, 123, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 41, 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]

(85, 85+37, 535)-Net over F₄ — Digital

Digital (85, 122, 535)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+37, 28052)-Net in Base 4 — Upper bound on s

There is no (85, 122, 28053)-net in base 4, because

1 times m-reduction [i] would yield (85, 121, 28053)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 071440 968745 853803 199992 357446 036124 683448 184090 978942 190437 718798 065550 > 4¹²¹ [i]