MinT - Best Known (157, 157+48, s)-Nets in Base 4

Best Known (157, 157+48, s)-Nets in Base 4

(157, 157+48, 1040)-Net over F₄ — Constructive and digital

Digital (157, 205, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (156, 204, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 51, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(157, 157+48, 2611)-Net over F₄ — Digital

Digital (157, 205, 2611)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+48, 453752)-Net in Base 4 — Upper bound on s

There is no (157, 205, 453753)-net in base 4, because

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]