MinT - Best Known (109−41, 109, s)-Nets in Base 7

Best Known (109−41, 109, s)-Nets in Base 7

(109−41, 109, 126)-Net over F₇ — Constructive and digital

Digital (68, 109, 126)-net over F₇, using

1 times m-reduction [i] based on digital (68, 110, 126)-net over F₇, using
- trace code for nets [i] based on digital (13, 55, 63)-net over F₄₉, using
  - net from sequence [i] based on digital (13, 62)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(109−41, 109, 540)-Net over F₇ — Digital

Digital (68, 109, 540)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−41, 109, 50649)-Net in Base 7 — Upper bound on s

There is no (68, 109, 50650)-net in base 7, because

1 times m-reduction [i] would yield (68, 108, 50650)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 18 650466 236268 692844 084528 183028 331063 142557 749254 146532 875190 800889 907722 889663 233166 033321 > 7¹⁰⁸ [i]