MinT - Best Known (58, 58+39, s)-Nets in Base 7

Best Known (58, 58+39, s)-Nets in Base 7

(58, 58+39, 118)-Net over F₇ — Constructive and digital

Digital (58, 97, 118)-net over F₇, using

1 times m-reduction [i] based on digital (58, 98, 118)-net over F₇, using
- trace code for nets [i] based on digital (9, 49, 59)-net over F₄₉, using
  - net from sequence [i] based on digital (9, 58)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(58, 58+39, 361)-Net over F₇ — Digital

Digital (58, 97, 361)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+39, 24593)-Net in Base 7 — Upper bound on s

There is no (58, 97, 24594)-net in base 7, because

1 times m-reduction [i] would yield (58, 96, 24594)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1347 763664 504154 477957 342835 655454 925837 472585 066478 045265 708991 349940 125534 475561 > 7⁹⁶ [i]