MinT - Best Known (133, 133+63, s)-Nets in Base 4

Best Known (133, 133+63, s)-Nets in Base 4

(133, 133+63, 240)-Net over F₄ — Constructive and digital

Digital (133, 196, 240)-net over F₄, using

2 times m-reduction [i] based on digital (133, 198, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 66, 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]

(133, 133+63, 619)-Net over F₄ — Digital

Digital (133, 196, 619)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+63, 25329)-Net in Base 4 — Upper bound on s

There is no (133, 196, 25330)-net in base 4, because

1 times m-reduction [i] would yield (133, 195, 25330)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2522 789530 536499 876458 445980 375649 184269 876561 488196 414839 404847 896787 107325 270243 851195 973761 233298 258125 566109 922992 > 4¹⁹⁵ [i]