MinT - Best Known (61, 61+46, s)-Nets in Base 7

Best Known (61, 61+46, s)-Nets in Base 7

(61, 61+46, 114)-Net over F₇ — Constructive and digital

Digital (61, 107, 114)-net over F₇, using

1 times m-reduction [i] based on digital (61, 108, 114)-net over F₇, using
- trace code for nets [i] based on digital (7, 54, 57)-net over F₄₉, using
  - net from sequence [i] based on digital (7, 56)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(61, 61+46, 291)-Net over F₇ — Digital

Digital (61, 107, 291)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+46, 13408)-Net in Base 7 — Upper bound on s

There is no (61, 107, 13409)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 667725 062351 365885 558138 425483 587881 274229 121984 523279 690000 120438 152625 564119 942498 851959 > 7¹⁰⁷ [i]