MinT - Best Known (52−30, 52, s)-Nets in Base 256

Best Known (52−30, 52, s)-Nets in Base 256

(52−30, 52, 521)-Net over F₂₅₆ — Constructive and digital

Digital (22, 52, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 18, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 34, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(52−30, 52, 967)-Net over F₂₅₆ — Digital

Digital (22, 52, 967)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−30, 52, 5620709)-Net in Base 256 — Upper bound on s

There is no (22, 52, 5620710)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 169230 623254 351138 963216 309152 954915 266501 101129 404495 530370 335989 669658 680511 924630 722524 655790 457062 941738 337306 014839 591376 > 256⁵² [i]