MinT - Best Known (72, 72+49, s)-Nets in Base 16

Best Known (72, 72+49, s)-Nets in Base 16

(72, 72+49, 536)-Net over F₁₆ — Constructive and digital

Digital (72, 121, 536)-net over F₁₆, using

1 times m-reduction [i] based on digital (72, 122, 536)-net over F₁₆, using
- trace code for nets [i] based on digital (11, 61, 268)-net over F₂₅₆, using
  - net from sequence [i] based on digital (11, 267)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(72, 72+49, 1379)-Net over F₁₆ — Digital

Digital (72, 121, 1379)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+49, 685272)-Net in Base 16 — Upper bound on s

There is no (72, 121, 685273)-net in base 16, because

1 times m-reduction [i] would yield (72, 120, 685273)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 121840 393733 601261 773868 467839 728595 143250 165083 564357 011832 564461 045733 308723 980651 494411 634684 480865 741467 983543 886160 347413 450534 886002 100381 > 16¹²⁰ [i]