MinT - Best Known (58, 58+45, s)-Nets in Base 7

Best Known (58, 58+45, s)-Nets in Base 7

(58, 58+45, 112)-Net over F₇ — Constructive and digital

Digital (58, 103, 112)-net over F₇, using

1 times m-reduction [i] based on digital (58, 104, 112)-net over F₇, using
- trace code for nets [i] based on digital (6, 52, 56)-net over F₄₉, using
  - net from sequence [i] based on digital (6, 55)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(58, 58+45, 264)-Net over F₇ — Digital

Digital (58, 103, 264)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+45, 12485)-Net in Base 7 — Upper bound on s

There is no (58, 103, 12486)-net in base 7, because

1 times m-reduction [i] would yield (58, 102, 12486)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 746668 275725 881142 403999 907949 360742 885384 816619 390972 234358 891768 085596 044482 391781 > 7¹⁰² [i]