MinT - Best Known (55−32, 55, s)-Nets in Base 256

Best Known (55−32, 55, s)-Nets in Base 256

(55−32, 55, 521)-Net over F₂₅₆ — Constructive and digital

Digital (23, 55, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 19, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 36, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(55−32, 55, 928)-Net over F₂₅₆ — Digital

Digital (23, 55, 928)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−32, 55, 5062007)-Net in Base 256 — Upper bound on s

There is no (23, 55, 5062008)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 2 839219 110778 830163 688950 479691 383538 763713 071457 258046 950529 268559 277560 282019 974560 105156 775019 740384 149043 502369 283972 142648 194391 > 256⁵⁵ [i]