MinT - Best Known (97−41, 97, s)-Nets in Base 16

Best Known (97−41, 97, s)-Nets in Base 16

(97−41, 97, 528)-Net over F₁₆ — Constructive and digital

Digital (56, 97, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (56, 98, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 49, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(97−41, 97, 894)-Net over F₁₆ — Digital

Digital (56, 97, 894)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−41, 97, 333408)-Net in Base 16 — Upper bound on s

There is no (56, 97, 333409)-net in base 16, because

1 times m-reduction [i] would yield (56, 96, 333409)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 402988 638065 161225 188960 521790 640171 355559 660016 835349 443993 518395 119738 164199 511910 114730 788710 925348 462693 699576 > 16⁹⁶ [i]