MinT - Best Known (157, 157+49, s)-Nets in Base 4

Best Known (157, 157+49, s)-Nets in Base 4

(157, 157+49, 1036)-Net over F₄ — Constructive and digital

Digital (157, 206, 1036)-net over F₄, using

4² times duplication [i] based on digital (155, 204, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 51, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(157, 157+49, 2420)-Net over F₄ — Digital

Digital (157, 206, 2420)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+49, 453752)-Net in Base 4 — Upper bound on s

There is no (157, 206, 453753)-net in base 4, because

1 times m-reduction [i] would yield (157, 205, 453753)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 360018 814545 619641 126388 139255 283204 079059 884697 991737 571187 585310 416610 295275 877283 682090 334418 385162 933306 256850 654991 > 4²⁰⁵ [i]