MinT - Best Known (42, 42+29, s)-Nets in Base 7

Best Known (42, 42+29, s)-Nets in Base 7

(42, 42+29, 112)-Net over F₇ — Constructive and digital

Digital (42, 71, 112)-net over F₇, using

1 times m-reduction [i] based on digital (42, 72, 112)-net over F₇, using
- trace code for nets [i] based on digital (6, 36, 56)-net over F₄₉, using
  - net from sequence [i] based on digital (6, 55)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(42, 42+29, 269)-Net over F₇ — Digital

Digital (42, 71, 269)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+29, 16926)-Net in Base 7 — Upper bound on s

There is no (42, 71, 16927)-net in base 7, because

1 times m-reduction [i] would yield (42, 70, 16927)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 143549 142202 641854 280230 948693 741154 256463 058949 966957 607917 > 7⁷⁰ [i]