MinT - Best Known (149, 149+49, s)-Nets in Base 4

Best Known (149, 149+49, s)-Nets in Base 4

(149, 149+49, 1028)-Net over F₄ — Constructive and digital

Digital (149, 198, 1028)-net over F₄, using

4² times duplication [i] based on digital (147, 196, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 49, 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]

(149, 149+49, 1926)-Net over F₄ — Digital

Digital (149, 198, 1926)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+49, 285838)-Net in Base 4 — Upper bound on s

There is no (149, 198, 285839)-net in base 4, because

1 times m-reduction [i] would yield (149, 197, 285839)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40348 842086 679127 841664 607912 097859 740910 682160 284029 783188 226505 225817 324783 874858 243176 833945 435217 205913 121727 977464 > 4¹⁹⁷ [i]