MinT - Best Known (58, 58+49, s)-Nets in Base 7

Best Known (58, 58+49, s)-Nets in Base 7

(58, 58+49, 108)-Net over F₇ — Constructive and digital

Digital (58, 107, 108)-net over F₇, using

1 times m-reduction [i] based on digital (58, 108, 108)-net over F₇, using
- trace code for nets [i] based on digital (4, 54, 54)-net over F₄₉, using
  - net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(58, 58+49, 225)-Net over F₇ — Digital

Digital (58, 107, 225)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+49, 8809)-Net in Base 7 — Upper bound on s

There is no (58, 107, 8810)-net in base 7, because

1 times m-reduction [i] would yield (58, 106, 8810)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 380765 526895 409888 772688 763964 379825 119429 500048 930173 558403 358171 621921 235644 573305 725873 > 7¹⁰⁶ [i]