MinT - Best Known (40, 40+37, s)-Nets in Base 7

Best Known (40, 40+37, s)-Nets in Base 7

(40, 40+37, 102)-Net over F₇ — Constructive and digital

Digital (40, 77, 102)-net over F₇, using

1 times m-reduction [i] based on digital (40, 78, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 39, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(40, 40+37, 144)-Net over F₇ — Digital

Digital (40, 77, 144)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+37, 4646)-Net in Base 7 — Upper bound on s

There is no (40, 77, 4647)-net in base 7, because

1 times m-reduction [i] would yield (40, 76, 4647)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 16935 410786 300749 198585 799313 006828 960812 922568 349999 559476 606245 > 7⁷⁶ [i]