MinT - Best Known (68, 68+42, s)-Nets in Base 7

Best Known (68, 68+42, s)-Nets in Base 7

(68, 68+42, 126)-Net over F₇ — Constructive and digital

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]

(68, 68+42, 506)-Net over F₇ — Digital

Digital (68, 110, 506)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+42, 38627)-Net in Base 7 — Upper bound on s

There is no (68, 110, 38628)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 914 040617 982677 722227 136043 184164 157920 121354 799894 173901 074656 310159 520884 373966 545209 376889 > 7¹¹⁰ [i]