MinT - Best Known (89−20, 89, s)-Nets in Base 4

Best Known (89−20, 89, s)-Nets in Base 4

(89−20, 89, 1036)-Net over F₄ — Constructive and digital

Digital (69, 89, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (68, 88, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 22, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(89−20, 89, 1756)-Net over F₄ — Digital

Digital (69, 89, 1756)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−20, 89, 344491)-Net in Base 4 — Upper bound on s

There is no (69, 89, 344492)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 383124 279194 662724 881160 517151 273602 946118 197187 383615 > 4⁸⁹ [i]