MinT - Best Known (103−43, 103, s)-Nets in Base 7

Best Known (103−43, 103, s)-Nets in Base 7

(103−43, 103, 116)-Net over F₇ — Constructive and digital

Digital (60, 103, 116)-net over F₇, using

1 times m-reduction [i] based on digital (60, 104, 116)-net over F₇, using
- trace code for nets [i] based on digital (8, 52, 58)-net over F₄₉, using
  - net from sequence [i] based on digital (8, 57)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(103−43, 103, 320)-Net over F₇ — Digital

Digital (60, 103, 320)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−43, 103, 18398)-Net in Base 7 — Upper bound on s

There is no (60, 103, 18399)-net in base 7, because

1 times m-reduction [i] would yield (60, 102, 18399)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 158 561852 880169 251907 114358 203152 057473 513431 855303 923404 765937 881013 788037 630207 566275 > 7¹⁰² [i]