MinT - Best Known (147, 147+49, s)-Nets in Base 4

Best Known (147, 147+49, s)-Nets in Base 4

(147, 147+49, 1028)-Net over F₄ — Constructive and digital

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]

(147, 147+49, 1819)-Net over F₄ — Digital

Digital (147, 196, 1819)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+49, 254651)-Net in Base 4 — Upper bound on s

There is no (147, 196, 254652)-net in base 4, because

1 times m-reduction [i] would yield (147, 195, 254652)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2521 928271 340191 003155 693477 672246 985513 818548 428968 278504 311665 019842 467429 716726 563313 207847 960794 390560 564998 217959 > 4¹⁹⁵ [i]