MinT - Best Known (166, 215, s)-Nets in Base 4

Best Known (166, 215, s)-Nets in Base 4

(166, 215, 1044)-Net over F₄ — Constructive and digital

Digital (166, 215, 1044)-net over F₄, using

1 times m-reduction [i] based on digital (166, 216, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 54, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(166, 215, 3131)-Net over F₄ — Digital

Digital (166, 215, 3131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 215, 763130)-Net in Base 4 — Upper bound on s

There is no (166, 215, 763131)-net in base 4, because

1 times m-reduction [i] would yield (166, 214, 763131)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 693 184869 912494 323532 832387 256421 517705 427963 596538 357390 204318 419003 291382 830750 031336 679920 624669 835203 718578 551493 955437 469779 > 4²¹⁴ [i]