MinT - Best Known (46, 46+41, s)-Nets in Base 7

Best Known (46, 46+41, s)-Nets in Base 7

(46, 46+41, 104)-Net over F₇ — Constructive and digital

Digital (46, 87, 104)-net over F₇, using

1 times m-reduction [i] based on digital (46, 88, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 44, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(46, 46+41, 170)-Net over F₇ — Digital

Digital (46, 87, 170)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+41, 5944)-Net in Base 7 — Upper bound on s

There is no (46, 87, 5945)-net in base 7, because

1 times m-reduction [i] would yield (46, 86, 5945)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4 771493 021279 116973 467997 836578 374181 435129 919539 635111 868472 548992 842657 > 7⁸⁶ [i]