MinT - Best Known (51, 51+48, s)-Nets in Base 7

Best Known (51, 51+48, s)-Nets in Base 7

(51, 51+48, 102)-Net over F₇ — Constructive and digital

Digital (51, 99, 102)-net over F₇, using

1 times m-reduction [i] based on digital (51, 100, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 50, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(51, 51+48, 169)-Net over F₇ — Digital

Digital (51, 99, 169)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+48, 4987)-Net in Base 7 — Upper bound on s

There is no (51, 99, 4988)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 462877 172037 704679 514933 271563 517994 690660 035051 270346 662424 393765 795245 451157 625281 > 7⁹⁹ [i]