MinT - Best Known (45, 45+42, s)-Nets in Base 7

Best Known (45, 45+42, s)-Nets in Base 7

(45, 45+42, 102)-Net over F₇ — Constructive and digital

Digital (45, 87, 102)-net over F₇, using

1 times m-reduction [i] based on digital (45, 88, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 44, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(45, 45+42, 156)-Net over F₇ — Digital

Digital (45, 87, 156)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+42, 4572)-Net in Base 7 — Upper bound on s

There is no (45, 87, 4573)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 33 413047 012889 511725 071822 488049 972862 780063 728748 111326 190578 176436 401199 > 7⁸⁷ [i]