MinT - Best Known (105−45, 105, s)-Nets in Base 7

Best Known (105−45, 105, s)-Nets in Base 7

(105−45, 105, 114)-Net over F₇ — Constructive and digital

Digital (60, 105, 114)-net over F₇, using

1 times m-reduction [i] based on digital (60, 106, 114)-net over F₇, using
- trace code for nets [i] based on digital (7, 53, 57)-net over F₄₉, using
  - net from sequence [i] based on digital (7, 56)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(105−45, 105, 290)-Net over F₇ — Digital

Digital (60, 105, 290)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−45, 105, 14903)-Net in Base 7 — Upper bound on s

There is no (60, 105, 14904)-net in base 7, because

1 times m-reduction [i] would yield (60, 104, 14904)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7767 801707 278244 859608 303803 355509 256846 933780 166893 500095 859020 950688 863263 830299 482129 > 7¹⁰⁴ [i]