MinT - Best Known (101, 101+33, s)-Nets in Base 4

Best Known (101, 101+33, s)-Nets in Base 4

(101, 101+33, 1028)-Net over F₄ — Constructive and digital

Digital (101, 134, 1028)-net over F₄, using

4² times duplication [i] based on digital (99, 132, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 33, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(101, 101+33, 1431)-Net over F₄ — Digital

Digital (101, 134, 1431)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+33, 229095)-Net in Base 4 — Upper bound on s

There is no (101, 134, 229096)-net in base 4, because

1 times m-reduction [i] would yield (101, 133, 229096)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 118 574093 820613 554313 987039 306650 349371 330334 626389 023745 412376 513211 678787 627874 > 4¹³³ [i]