MinT - Best Known (88−20, 88, s)-Nets in Base 4

Best Known (88−20, 88, s)-Nets in Base 4

(88−20, 88, 1036)-Net over F₄ — Constructive and digital

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]

(88−20, 88, 1633)-Net over F₄ — Digital

Digital (68, 88, 1633)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−20, 88, 299896)-Net in Base 4 — Upper bound on s

There is no (68, 88, 299897)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 95782 057780 466523 818428 745089 597437 287467 125746 982376 > 4⁸⁸ [i]