MinT - Best Known (133, 198, s)-Nets in Base 4

Best Known (133, 198, s)-Nets in Base 4

(133, 198, 240)-Net over F₄ — Constructive and digital

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, 198, 577)-Net over F₄ — Digital

Digital (133, 198, 577)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 198, 21660)-Net in Base 4 — Upper bound on s

There is no (133, 198, 21661)-net in base 4, because

1 times m-reduction [i] would yield (133, 197, 21661)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40382 274938 135376 434927 668058 589727 453674 212600 010340 491675 305716 522033 430421 602026 981981 074605 933411 449523 767974 736900 > 4¹⁹⁷ [i]