MinT - Best Known (65−31, 65, s)-Nets in Base 7

Best Known (65−31, 65, s)-Nets in Base 7

(65−31, 65, 102)-Net over F₇ — Constructive and digital

Digital (34, 65, 102)-net over F₇, using

1 times m-reduction [i] based on digital (34, 66, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 33, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(65−31, 65, 130)-Net over F₇ — Digital

Digital (34, 65, 130)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−31, 65, 4309)-Net in Base 7 — Upper bound on s

There is no (34, 65, 4310)-net in base 7, because

1 times m-reduction [i] would yield (34, 64, 4310)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1 222533 988569 817263 762987 078081 727396 353410 468905 535185 > 7⁶⁴ [i]