MinT - Best Known (89−43, 89, s)-Nets in Base 7

Best Known (89−43, 89, s)-Nets in Base 7

(89−43, 89, 102)-Net over F₇ — Constructive and digital

Digital (46, 89, 102)-net over F₇, using

1 times m-reduction [i] based on digital (46, 90, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 45, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(89−43, 89, 158)-Net over F₇ — Digital

Digital (46, 89, 158)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−43, 89, 5018)-Net in Base 7 — Upper bound on s

There is no (46, 89, 5019)-net in base 7, because

1 times m-reduction [i] would yield (46, 88, 5019)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 234 568947 508894 167206 426002 456900 878339 027232 878277 189770 252581 088248 213035 > 7⁸⁸ [i]