MinT - Best Known (44, 85, s)-Nets in Base 7

Best Known (44, 85, s)-Nets in Base 7

(44, 85, 102)-Net over F₇ — Constructive and digital

Digital (44, 85, 102)-net over F₇, using

1 times m-reduction [i] based on digital (44, 86, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 43, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(44, 85, 153)-Net over F₇ — Digital

Digital (44, 85, 153)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 85, 4891)-Net in Base 7 — Upper bound on s

There is no (44, 85, 4892)-net in base 7, because

1 times m-reduction [i] would yield (44, 84, 4892)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 97581 201972 141245 993999 815607 670681 443185 304477 145273 138479 105713 016257 > 7⁸⁴ [i]