MinT - Best Known (88−40, 88, s)-Nets in Base 7

Best Known (88−40, 88, s)-Nets in Base 7

(88−40, 88, 108)-Net over F₇ — Constructive and digital

Digital (48, 88, 108)-net over F₇, using

trace code for nets [i] based on digital (4, 44, 54)-net over F₄₉, using
- net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(88−40, 88, 198)-Net over F₇ — Digital

Digital (48, 88, 198)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−40, 88, 7224)-Net in Base 7 — Upper bound on s

There is no (48, 88, 7225)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 233 917698 303759 070074 803566 728270 029934 969432 853772 087276 526435 703894 987681 > 7⁸⁸ [i]