MinT - Best Known (46, 46+39, s)-Nets in Base 7

Best Known (46, 46+39, s)-Nets in Base 7

(46, 46+39, 106)-Net over F₇ — Constructive and digital

Digital (46, 85, 106)-net over F₇, using

1 times m-reduction [i] based on digital (46, 86, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 43, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(46, 46+39, 186)-Net over F₇ — Digital

Digital (46, 85, 186)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+39, 7187)-Net in Base 7 — Upper bound on s

There is no (46, 85, 7188)-net in base 7, because

1 times m-reduction [i] would yield (46, 84, 7188)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 97561 821690 706759 969086 719997 430295 159453 044125 572077 270953 119459 810017 > 7⁸⁴ [i]