MinT - Best Known (87−40, 87, s)-Nets in Base 7

Best Known (87−40, 87, s)-Nets in Base 7

(87−40, 87, 106)-Net over F₇ — Constructive and digital

Digital (47, 87, 106)-net over F₇, using

1 times m-reduction [i] based on digital (47, 88, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 44, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(87−40, 87, 188)-Net over F₇ — Digital

Digital (47, 87, 188)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−40, 87, 6553)-Net in Base 7 — Upper bound on s

There is no (47, 87, 6554)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 33 420234 275443 615104 619091 063370 737179 705330 008006 165943 648394 856979 291561 > 7⁸⁷ [i]