MinT - Best Known (99−41, 99, s)-Nets in Base 7

Best Known (99−41, 99, s)-Nets in Base 7

(99−41, 99, 116)-Net over F₇ — Constructive and digital

Digital (58, 99, 116)-net over F₇, using

1 times m-reduction [i] based on digital (58, 100, 116)-net over F₇, using
- trace code for nets [i] based on digital (8, 50, 58)-net over F₄₉, using
  - net from sequence [i] based on digital (8, 57)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(99−41, 99, 321)-Net over F₇ — Digital

Digital (58, 99, 321)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−41, 99, 19135)-Net in Base 7 — Upper bound on s

There is no (58, 99, 19136)-net in base 7, because

1 times m-reduction [i] would yield (58, 98, 19136)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 66030 639851 978486 193767 594883 927106 938433 934947 525594 409854 858111 356471 354862 284289 > 7⁹⁸ [i]